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A sadistic predator who admittedly raped a missionary worker inside NYU’s Catholic Center five weeks ago is already in jail on a separate robbery charges, cops said today after matching DNA evidence he left behind.

Investigators were able to link Michael Johnson, 30, to DNA evidence that was lifted from a hat that was left at the scene when the NYU missionary worker was raped Oct. 31.

Sources said Johnson confessed.

The suspect allegedly followed the victim, a 24-year-old woman from Ohio, as she walked to the NYU Catholic Center on Thompson Street. He told investigators he was high and drunk and only intended to rob her, the sources said.

That’s when Johnson allegedly punched her in the back of the head and chest repeatedly before he pushed her inside the building.

The victim pleaded as she repeated the ‘Hail Mary’ prayer before he snarled, “I should have killed you, too,” sources said.

He left his fedora behind.

The creep told cops he took her clothes off to prevent her from going to authorities.

Johnson has not yet been charged, and his case is expected to go before a grand jury today.

Johnson was caught after a robbery at a CD store in Midtown when security saw him allegedly stuffing items from a display rack into his pockets at 306 W. 54 St.

But the suspect left his identification behind after he punched a store clerk and fled the scene, cops said.